Which of the following numbers is a multiple of 8? ${41,49,57,72,93}$
Explanation: The multiples of $8$ are $8$ $16$ $24$ $32$ ..... In general, any number that leaves no remainder when divided by $8$ is considered a multiple of $8$ We can start by dividing each of our answer choices by $8$ $41 \div 8 = 5\text{ R }1$ $49 \div 8 = 6\text{ R }1$ $57 \div 8 = 7\text{ R }1$ $72 \div 8 = 9$ $93 \div 8 = 11\text{ R }5$ The only answer choice that leaves no remainder after the division is $72$ $ 9$ $8$ $72$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $72$ $72 = 2\times2\times2\times3\times3 8 = 2\times2\times2$ Therefore the only multiple of $8$ out of our choices is $72$. We can say that $72$ is divisible by $8$.